Linear Algebra: Basis and Dimension

10. Find the coordinate vector of p relative to the basis S = {p1, p2, p3}.

(a) p = 4 - 3x + x2; p1 = 1, p2 = x, p3 = x2
(b) p = 2 - x + x2; p1 = 1 + x, p2 = 1 + x2, p3 = x + x2

22. Find the standard basis vectors that can be added to the set {v1, v2} to produce a basis for R4.

v1 = (1, -4, 2, -3), v2 = (-3, 8, -4, 6)

30. Prove: Any subspace of a finite-dimensional vector space is finite-dimensional.
Hint: You can do a proof by contradiction by using 2 or 3 Theorems from section.

See attached file for full problem description.

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